METHOD 1
Convert to improper fractions: 18/7-X=14/9
Multiply through by LCD=63: 162-63X=98 (18/7*63=9*18=162; 14/9*63=14*7=98)
Add 63X to each side: 162=98+63X
Subtract 98 from each side: 64=63X, X=64/63=1 1/63
METHOD 2
Add X to each side: 2 4/7=1 5/9+X
Subtract 1 5/9 from each side: 2 4/7 - 1 5/9 = X
Subtract whole numbers on left first: 2-1=1; to subtract fractions, use LCD=63: 4/7-5/9=(36-35)/63=1/63 and put in the whole number 1: 1 1/63. You've now calculated the difference between the mixed numbers.
So now put this answer into the equation: 1 1/63=X or X=1 1/63.
Method 2 uses smaller numbers and you may prefer that.